If we let  and  represent the number of large and small boxes sold, respectively, since 305 boxes were sold, one linear equation of the 2x2 system will be

The money raised from the sale of  large boxes of cookies, each of which cost $4.75, is ; the money raised from the sale of  small boxes of cookies, each of which cost $3.25, is . The total money raised is $1,196.75, so the other linear equation of the system is 

The augmented matrix of this system will comprise the coefficients of these equations, both of which are in standard form, so the matrix will be

If we let  and  represent the amount of the weaker and stronger solutions, respectively, since the chemist needs 1 liter of the resulting solution, one linear equation of the 2x2 system will be 

The amount of alcohol in  liters of a 10% solution will be ; the amount of alcohol in  liters of a 40% solution will be ; and the total amount of alcohol in the resulting solution will be 20 % of a liter, or 0.20 liters. Therefore, the second linear equation of the system will be

The augmented matrix of this system will comprise the coefficients of these equations, both of which are in standard form, so the matrix will be

,

which is the correct choice.

To find the number of blue items Jon has, we sum the entries in the column labelled  and get . Recall that matrices are organized by rows and columns where each entry refers to the number of items that are, in this case, both of the same color AND type. All the entries in any one column are of the same color. All of the entries in any row are of the same clothing type.  

If Jon has three red shirts and two blue pants. The total number of combinations of one shirt and one pair of pants he can wear is going to be the number of shirts he can wear with the first pair of pants, , plus the number of shirt he can wear with the second pair of pants, also . That sums to  total outfits.

If the barista mixes  pounds of Peppermint Nirvana and  pounds of Strawberry Fields to make twenty pounds of tea total, then

will be one of the equations in the system.

 pounds of Peppermint Nirvana tea for $12 a pound will cost a total of  dollars;  pounds of Strawberry Fields tea will cost a total of  dollars. Tewnty pounds of the Strawberry Peppermint Delight tea for $13 a pound will cost  dollars. Since the tea will sell for the same price blended as separate, the other equation of the system will be

The augmented matrix of this system will comprise the coefficients of these equations, both of which are in standard form, so the matrix will be

.

Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:

Now, just simplify:

There is your answer!

Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:

Then, just simplify all of those simple additions and subtractions:

To add matrices you simply add the numbers in the same position as each other.

Plugging the given values into the above formula, we are able to solve the question.

When subtracting matrices, you want to subtract each corresponding cell.

Now solve for  and 

You can treat matrices just like you treat other members of an equation. Therefore, you can subtract the matrix

from both sides of the equation.  This gives you:

Now, matrix subtraction is simple. You merely subtract each element, matching the correlative spaces with each other:

Then, you simplify:

Therefore,